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Novel soliton molecules and breather-positon on zero background for the complex modified KdV equation

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Abstract

Based on Darboux transformation, we generate breather solutions sitting on zero background via module resonance for complex modified KdV equation. Then, some novel soliton molecules, breather molecules and breather-soliton molecules are obtained theoretically by module resonance and velocity resonance. Further, we study the higher-order breather-positons with zero background on the basis of degenerate Darboux transformation and module resonance for the first time. We discuss the dynamics of higher-order breather-positons in detail and propose related propositions. Finally, we find new elastic interactions between smooth positons and breather-positons by means of degenerate Darboux transformation and partial module resonance.

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Acknowledgements

This work is supported by National Natural Science Foundation of China under Grant No. 11775121 and K.C. Wong Magna Fund in Ningbo University. The authors would like to express their sincere thanks to Professor S.Y. Lou for his guidance and encouragement.

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  1. School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, People’s Republic of China

    Zhao Zhang, Xiangyu Yang & Biao Li

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  1. Zhao Zhang
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  2. Xiangyu Yang
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  3. Biao Li
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Correspondence to Biao Li .

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Zhang, Z., Yang, X. & Li , B. Novel soliton molecules and breather-positon on zero background for the complex modified KdV equation. Nonlinear Dyn 100, 1551–1557 (2020). https://doi.org/10.1007/s11071-020-05570-1

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